My bibliography  Save this article

# Sophisticated imitation in cyclic games

## Author

Listed:
• Josef Hofbauer

() (Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria)

• Karl H. Schlag

() (Economics Department, European University Institute, Via dei Roccettini 9, 50016 San Domenico di Fiesole, Italy)

## Abstract

Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finite sample of other outcomes within their population. Individuals from the same population follow the same behavioral rule. In the resulting discrete time dynamics the unique Nash equilibrium is unstable. However, for sample sizes greater than one, we present an imitation rule where long run play cycles closely around the equilibrium.

## Suggested Citation

• Josef Hofbauer & Karl H. Schlag, 2000. "Sophisticated imitation in cyclic games," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 523-543.
• Handle: RePEc:spr:joevec:v:10:y:2000:i:5:p:523-543
as

## Download full text from publisher

File URL: http://link.springer.de/link/service/journals/00191/papers/0010005/00100523.pdf
Download Restriction: Access to the full text of the articles in this series is restricted

As the access to this document is restricted, you may want to search for a different version of it.

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as

Cited by:

1. Luckraz, Shravan, 2013. "On innovation cycles in a finite discrete R&D game," Economic Modelling, Elsevier, vol. 30(C), pages 510-513.
2. Offerman, Theo & Schotter, Andrew, 2009. "Imitation and luck: An experimental study on social sampling," Games and Economic Behavior, Elsevier, vol. 65(2), pages 461-502, March.
3. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
4. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
5. Alanyali, Murat, 2010. "A note on adjusted replicator dynamics in iterated games," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 86-98, January.
6. Ana B. Ania, 2000. "Learning by Imitation when Playing the Field," Vienna Economics Papers 0005, University of Vienna, Department of Economics.
7. Lipatov, Vilen, 2003. "Evolution of Tax Evasion," MPRA Paper 966, University Library of Munich, Germany, revised 06 Dec 2005.

## More about this item

### Keywords

Strictly improving - Matching pennies game - Replicator dynamics - Limit cycle - Discretization;

### JEL classification:

• C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

### Statistics

Access and download statistics

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joevec:v:10:y:2000:i:5:p:523-543. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

We have no references for this item. You can help adding them by using this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.